Though I do admit that one would be in a bit of a pickle if the 12v charging circuitry stopped working (melted/blew-up/smoked/fried). Who knows if that is water cooled or not and has temperature/overload protection.
You should be OK with the Leaf fully on and in park. The DC/DC converter will keep the 12v circuit energized at about 13.5 volts once the battery is topped up, and will drive your DC-AC inverter for as long as the 400v main pack holds out. (Probably a good idea to monitor it, but the Leaf will shut off when it's depleted.)
The DC/DC converter is water-cooled with a radiator and fan; it will be fine. Make sure your climate control is "off" or you'll drain your traction battery a lot faster than you'd like and to no purpose.
Hook up your inverter to the battery terminals or the + terminal and the chassis. I have tested this arrangement to about 100 amps (roughly 1100 watts with typical losses) and it works as long as the traction battery is engaged. Without it, you'll drain your 12v battery like no one's business and once that's dead, so will be your Leaf. Even with a jump start, fully draining most lead acid batteries is a BAD IDEA, especially if you leave it discharged for any length of time. I don't think they stock the car with a deep-cycle 12v battery.
The Leaf does automatically charge its 12v battery, but only after 5 days of non-operation. I don't think it will do so more frequently than that, even if the battery gets low. You can try it and see, but as I said, it isn't a good idea to draw down your 12v battery in general.
Overall, the DC-AC converter is a great "emergency plan" for major power outages, but probably not something you should do on a daily basis.